Using self organizing maps on compositional data

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Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed
to explore patterns in high-dimensional multivariate data. The conventional version
of the algorithm involves the use of Euclidean metric in the process of adaptation of
the model vectors, thus rendering in theory a whole methodology incompatible ...[+]

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed
to explore patterns in high-dimensional multivariate data. The conventional version
of the algorithm involves the use of Euclidean metric in the process of adaptation of
the model vectors, thus rendering in theory a whole methodology incompatible with
non-Euclidean geometries.
In this contribution we explore the two main aspects of the problem:
1. Whether the conventional approach using Euclidean metric can shed valid results
with compositional data.
2. If a modification of the conventional approach replacing vectorial sum and scalar
multiplication by the canonical operators in the simplex (i.e. perturbation and
powering) can converge to an adequate solution.
Preliminary tests showed that both methodologies can be used on compositional data.
However, the modified version of the algorithm performs poorer than the conventional
version, in particular, when the data is pathological. Moreover, the conventional ap-
proach converges faster to a solution, when data is \well-behaved".
Key words: Self Organizing Map; Artificial Neural networks; Compositional data[-]